Nishiwaki S
Appl Opt. 1995 Nov 1;34(31):7361-71. doi: 10.1364/AO.34.007361.
The convergence characteristics of the previously proposed concentric-circular focusing grating coupler (CFGC) are analyzed, and aberration functions for such typical errors as wavelength errors, effective index errors, grating pattern distortion, and CFGC eccentricity are derived for evaluation of their allowances. The analyzed results prove that the Strehl intensity deterioration caused by a wavelength error and an effective index offset can be minimized by optimization of the annular aperture of the CFGC. In the case of Marechal's criterion, a wavelength error of ±8.6% at the annular aperture of NA = 0.440-0.607 and an effective index error of ±20.4% at NA = 0.500-0.652 are permissible, and these values are ∼100 times greater than those that are seen in a conventional focusing grating coupler that has a rotationally asymmetrical structure with respect to its optical axis.
分析了先前提出的同心圆形聚焦光栅耦合器（CFGC）的收敛特性，并推导了诸如波长误差、有效折射率误差、光栅图案畸变和CFGC偏心等典型误差的像差函数，以评估其容差。分析结果表明，通过优化CFGC的环形孔径，可以将由波长误差和有效折射率偏移引起的斯特列尔强度劣化降至最低。在马雷夏尔判据的情况下，在数值孔径（NA）为0.440 - 0.607的环形孔径处，波长误差±8.6%是允许的，在NA为0.500 - 0.652时，有效折射率误差±20.4%是允许的，这些值比具有相对于其光轴旋转不对称结构的传统聚焦光栅耦合器中的值大~100倍。
